1. Field of the Invention
The present invention relates to temperature compensation of quartz crystal oscillators.
2. Description of the Prior Art
Crystal oscillators generally comprise a resonant circuit, including a crystal and a load capacitance, and means, such as an amplifier, for supplying energy to the resonant circuit to make up for losses and so sustain oscillations in the resonant circuit. The crystal load capacitance conventionally is adjustable typically including a voltage-controlled-capacitance device such as a varactor diode, to provide for adjustment of the resonant frequency of the circuit.
Quartz crystals of the AT cut type are widely used in crystal oscillators. The self-resonant frequency of such AT cut crystals, however, varies in accordance with changes in temperature. The self-resonant frequency versus temperature characteristic of AT cut crystals is dependent on the relative position of the parallel surfaces of the quartz crystal with respect to the crystallographic axes of the quartz, and is expressed as a third degree polynominal such as follows: EQU .DELTA.F = [A.sub.o .DELTA.T + B.sub.o T.sup.2 + C.sub.o .DELTA.T.sup.3 ] F.sub.R ( 1)
where F.sub. R is the self-resonant frequency of the crystal at a reference temperature T.sub. R, .DELTA.F is equal to the self-resonant frequency excursion with respect to F.sub. of the crystal at the instantaneous temperature T and .DELTA.T is the temperature excursion from the reference temperature to the instantaneous temperature. Reference temperature T.sub.R is generally taken to be 26.degree. C for an AT cut crystal. Coefficients A.sub.o, B.sub.o and C.sub.o are dependent upon the relative position of the parallel surfaces of the particular crystal with respect to the crystallographic axis of the quartz, and in particular, with respect to the "Z" or optical axis of the quartz.
Compensation for change in self-resonant frequency due to temperature change, hereinafter referred to as "frequency drift," is generally accomplished by varying the crystal load capacitance, i.e., the capacitance across the crystal, in a predetermined manner. The change in crystal load capacitance is typically effected by application of a temperature-dependent biasing voltage to a voltage-controlled capacitance device. In the prior art, however, full compensation of the drift characteristics of AT crystals have been limited to crystals with temperature drift characteristics having only one point of inflection within the operating temperature range, and utilize compensation networks having a large number of components. Further, the prior art compensation networks have typically neglected the second order term in the crystal drift characteristic equation. The temperature dependent bias signal is typically produced by a temperature-dependent potential-dividing network, a bridge network utilizing a plurality of variable-capacitance devices, or both. Examples of such prior art are described in U.S. Pat. Nos. 3,054,966 issued Sept. 18, 1962 to R. Etherington; 3,409,841 issued Nov. 5, 1968 to R. Munn; 3,525,055 issued Aug. 18, 1970 to P. Mrozek; and 3,581,239 issued May 25, 1971 to W. Knutson.